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Suppose there are two congruent disks rotating at its center in opposite directions at the same magnitude, and a ball is put into the spacing between the two disks to be shot out. The ball was a rest before the collision, so it has no momentum to begin with. The ball collides with the two disks at the same time, and momentum is conserved

The moment of inertia of the two spinning disks are 1/2MR^2 due to it being two solid disks rotating on its center axis.

I am trying to find out how the radius, angular velocity, and mass of two equal spinning disks impacts the exit velocity of the ball, however the radius of the disks keep canceling out. I know the radius must impact the speed, so I’m guessing my approach was wrong. Could anyone help me on this? Thank you.

enter image description here

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closed as off-topic by Aaron Stevens, John Rennie, Kyle Kanos, Jon Custer, ZeroTheHero Jan 2 at 22:40

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    $\begingroup$ Welcome to Physics SE! I think that more detail is needed to specify what's happening. Are the centres of the disks fixed? If so, what is $P_{\text{disk}}$? Is the ball initially moving? There seems to be a $v_{\text{ball}}$ but no $P_{\text{ball}}$, only $P_{\text{ball}}'$. Is energy conserved? You haven't included an equation for it. Is the ball supposed to be in contact with the two disks simultaneously, just at the same instant of time? If you can edit your question to clarify what assumptions you are making, this might help. $\endgroup$ – user197851 Dec 30 '18 at 14:48
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    $\begingroup$ This is still confusing. What information are you given? If momentum is conserved then you need to know what the speed of the disks are before and after the collision to know what happens to the ball. Is this given? Also keep in mind that linear momentum and angular momentum are two different things. It looks like you are trying to combine them into one conservation law. $\endgroup$ – Aaron Stevens Jan 2 at 5:01
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This seems to be a simple math error: $$\frac{a}{c}-\frac{b}{c}=\frac{a-b}{c}$$ The radius does not cancel.

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